Question

y=(2x+3) underoot of x --------------differentiate it. w.r.t x

Answer 1

Answer on Question #47287 - Math - Calculus

y = (2x + 3)

underoot of x ---differentiate it. w.r.t x

Solution:

We have $\left(\varphi (x)*\psi (x)\right)' = \varphi (x)*\psi '(x) + \varphi '(x)*\psi (x).$

Also $y = (2x + 3)*\sqrt{x}$ . Hence

$$\begin{array}{l} \frac {d y}{d x} = y ^ {\prime} = \left((2 x + 3) * \sqrt {x}\right) ^ {\prime} = (2 x + 3) ^ {\prime} * \sqrt {x} + (2 x + 3) * (\sqrt {x}) ^ {\prime} = \\ = 2 \sqrt {x} + \frac {(2 x + 3)}{2 \sqrt {x}} = \frac {(6 x + 3)}{2 \sqrt {x}} \\ \end{array}$$

Answer: $y' = \frac{(6x + 3)}{2\sqrt{x}}$

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